> For example, if surgeons knew their success rate were public, they would be incentivized to take easier cases. Who would take a difficult case if they knew it would constitute a bad mark on their record almost for sure?

Why would it be a "bad mark" if everyone understood the case was difficult? Given a difficult case, wouldn't a surgeon be graded badly only if they did poorer on average than other surgeons tackling similar cases?

As long as a case's "difficulty" is measured in a consistent way, I don't see how surgeons would be incentivized to avoid difficult cases.